BIFURCATIONS OF NORMALLY HYPERBOLIC INVARIANT MANIFOLDS IN ANALYTICALLY TRACTABLE MODELS AND CONSEQUENCES FOR REACTION DYNAMICS

DOI10.1142/S0218127413300437zbMath1284.37027arXiv1304.3947OpenAlexW3105429002MaRDI QIDQ5407265

Gregory S. Ezra, Frédéric A. L. Mauguière, Stephen Wiggins, Peter J. Collins

Publication date: 7 April 2014

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3947

zbMATH Keywords

bifurcationnormally hyperbolic invariant manifoldtransition state theoryreaction dynamicsphase space dividing surface

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37Jxx) Local and nonlocal bifurcation theory for dynamical systems (37Gxx)

Related Items (7)

The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics ⋮ Can we understand the branching of reaction valleys for more than two degrees of freedom? ⋮ Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface ⋮ Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics ⋮ Hamiltonian pitchfork bifurcation in transition across index-1 saddles ⋮ Controlling reaction dynamics in chemical model systems through external driving ⋮ Bifurcation of Dividing Surfaces Constructed from a Pitchfork Bifurcation of Periodic Orbits in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation

Cites Work

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• Direct construction of a dividing surface of minimal flux for multi-degree-of-freedom systems that cannot be recrossed
• Wigner's dynamical transition state theory in phase space: classical and quantum
• Invariant manifolds
• Reaction rate theory: What it was, where is it today, and where is it going?
• A formula to compute the microcanonical volume of reactive initial conditions in transition state theory
• Remarks on the definition of hyperbolic tori of Hamiltonian systems

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